L. David and . Donoho, Compressed sensing, IEEE Transactions on information theory, vol.52, issue.4, pp.1289-1306, 2006.

J. Emmanuel, T. Candes, and . Tao, Near-optimal signal recovery from random projections: Universal encoding strategies?, IEEE transactions on information theory, vol.52, pp.5406-5425, 2006.

I. Goodfellow, J. Pouget-abadie, M. Mirza, B. Xu, D. Warde-farley et al., Generative adversarial nets, Advances in neural information processing systems, pp.2672-2680, 2014.

A. Eric-w-tramel, F. Drémeau, and . Krzakala, Approximate message passing with restricted Boltzmann machine priors, Journal of Statistical Mechanics: Theory and Experiment, issue.7, p.73401, 2016.

W. Eric, A. Tramel, F. Manoel, M. Caltagirone, F. Gabrié et al., Inferring sparsity: Compressed sensing using generalized restricted Boltzmann machines, 2016 IEEE Information Theory Workshop (ITW), pp.265-269, 2016.

A. Bora, A. Jalal, E. Price, and A. Dimakis, Compressed sensing using generative models, Proceedings of the 34th International Conference on Machine Learning, vol.70, pp.537-546, 2017.

A. Manoel, F. Krzakala, M. Mézard, and L. Zdeborová, Multi-layer generalized linear estimation, 2017 IEEE International Symposium on Information Theory (ISIT), pp.2098-2102, 2017.
URL : https://hal.archives-ouvertes.fr/cea-01447203

P. Hand and V. Voroninski, Global guarantees for enforcing deep generative priors by empirical risk, Conference On Learning Theory, pp.970-978, 2018.

A. Fletcher, S. Rangan, and P. Schniter, Inference in deep networks in high dimensions, 2018 IEEE International Symposium on Information Theory (ISIT), pp.1884-1888, 2018.

P. Hand, O. Leong, and V. Voroninski, Phase retrieval under a generative prior, Advances in Neural Information Processing Systems, pp.9136-9146, 2018.

G. Dustin, S. Mixon, and . Villar, Sunlayer: Stable denoising with generative networks, 2018.

B. Aubin, B. Loureiro, A. Maillard, F. Krzakala, and L. Zdeborová, The spiked matrix model with generative priors, Advances in Neural Information Processing Systems, vol.32, pp.8364-8375, 2019.

G. Reeves, Additivity of information in multilayer networks via additive gaussian noise transforms, 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp.1064-1070, 2017.

M. Gabrié, A. Manoel, C. Luneau, N. Macris, F. Krzakala et al., Entropy and mutual information in models of deep neural networks, Advances in Neural Information Processing Systems, pp.1821-1831, 2018.

J. Emmanuel, Y. C. Candes, T. Eldar, V. Strohmer, and . Voroninski, Phase retrieval via matrix completion, SIAM review, vol.57, issue.2, pp.225-251, 2015.

P. Netrapalli, P. Jain, and S. Sanghavi, Phase retrieval using alternating minimization, Advances in Neural Information Processing Systems, pp.2796-2804, 2013.

Y. Wu and S. Verdú, Optimal phase transitions in compressed sensing, IEEE Transactions on Information Theory, vol.58, issue.10, pp.6241-6263, 2012.

F. Krzakala, M. Mézard, F. Sausset, Y. F. Sun, and L. Zdeborová, Statistical physics based reconstruction in compressed sensing, Physical Review X, vol.2, issue.2, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00716897

G. Reeves and M. Gastpar, Compressed sensing phase transitions: Rigorous bounds versus replica predictions, 46th Annual Conference on Information Sciences and Systems (CISS), pp.1-6, 2012.

L. Zdeborová and F. Krzakala, Statistical physics of inference: Thresholds and algorithms, Advances in Physics, vol.65, issue.5, pp.453-552, 2016.

J. Barbier, M. Dia, N. Macris, and F. Krzakala, The mutual information in random linear estimation, 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp.625-632, 2016.

G. Reeves and H. D. Pfister, The replica-symmetric prediction for compressed sensing with gaussian matrices is exact, 2016 IEEE International Symposium on Information Theory (ISIT), pp.665-669, 2016.

J. Barbier, F. Krzakala, N. Macris, L. Miolane, and L. Zdeborová, Optimal errors and phase transitions in high-dimensional generalized linear models, Proceedings of the National Academy of Sciences, vol.116, pp.5451-5460, 2019.

M. Mézard, G. Parisi, and M. Virasoro, Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications, vol.9, 1987.

A. David-l-donoho, A. Maleki, and . Montanari, Message-passing algorithms for compressed sensing, Proceedings of the National Academy of Sciences, vol.106, issue.45, pp.18914-18919, 2009.

. Sundeep-rangan, Generalized approximate message passing for estimation with random linear mixing, 2011 IEEE International Symposium on Information Theory Proceedings, pp.2168-2172, 2011.

P. Schniter and S. Rangan, Compressive phase retrieval via generalized approximate message passing, IEEE Transactions on Signal Processing, vol.63, issue.4, pp.1043-1055, 2014.

A. Christopher, . Metzler, K. Manoj, S. Sharma, . Nagesh et al., Coherent inverse scattering via transmission matrices: Efficient phase retrieval algorithms and a public dataset, 2017 IEEE International Conference on Computational Photography (ICCP), pp.1-16, 2017.

M. Bayati and A. Montanari, The dynamics of message passing on dense graphs, with applications to compressed sensing, IEEE Transactions on Information Theory, vol.57, issue.2, pp.764-785, 2011.

F. Krzakala, M. Mézard, F. Sausset, Y. Sun, and L. Zdeborová, Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices, Journal of Statistical Mechanics: Theory and Experiment, vol.2012, issue.08, p.8009, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00764645

Y. Kabashima, Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels, Journal of Physics: Conference Series, vol.95, p.12001, 2008.

J. Barbier, N. Macris, A. Maillard, and F. Krzakala, The mutual information in random linear estimation beyond iid matrices, 2018 IEEE International Symposium on Information Theory (ISIT), pp.1390-1394, 2018.

R. Dudeja, J. Ma, and A. Maleki, Information theoretic limits for phase retrieval with subsampled Haar sensing matrices, 2019.